Bellman Ford - ベルマンフォード法
(Library/Graph/BellmanFord.hpp)

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Last update: 2026-02-13 15:23:31+09:00
Include: #include "Library/Graph/BellmanFord.hpp"

Bellman Ford - ベルマンフォード法

頂点数 $V$ 辺数 $E$ のグラフにおける単一始点最短経路問題をベルマンフォード法を用いて解きます。

Function

Constructor

BellmanFord(Graph<WeightType> &graph, Vertex s = -1)

グラフ $G$ を頂点数 $V$ 辺数 $E$ の graph で初期化します。
始点頂点 $s$ を指定すると、初期化後に Solve(s) を呼び出します。

制約

$-1 \le s \lt V$

計算量

$\textrm{O}(V)$

Reachable

inline bool Reachable(const Vertex &t) const

頂点 $s$ から頂点 $t$ に到達可能であるかを判定します。

制約

$0 \le t \lt V$
Solve() が $1$ 回以上呼び出されている

計算量

$\textrm{O}(1)$

Distance

inline WeightType Distance(const Vertex &t) const

頂点 $s$ から頂点 $t$ への最短経路長を返します。
頂点 $t$ に到達不能であるとき、INF を返します。

制約

$0 \le t \lt V$
Solve() が $1$ 回以上呼び出されている

計算量

$\textrm{O}(1)$

NegativeCycle

inline bool NegativeCycle() const

$G$ が負閉路を含むかを判定します。

制約

Solve() が $1$ 回以上呼び出されている

計算量

$\textrm{O}(1)$

Solve

void Solve(Vertex s)

頂点 $s$ を始点とした単一始点最短経路問題を解きます。

制約

$0 \le s \lt V$

計算量

$\textrm{O}(VE)$

operator[]

(1) WeightType operator[](const Vertex &t)
(2) const WeightType operator[](const Vertex &t) const 

Distance(t) を返します。

制約

$0 \le t \lt V$
Solve(s) が $1$ 回以上呼び出されている

計算量

$\textrm{O}(1)$

Depends on

Verified with

verify/AOJ-GRL-1-B.test.cpp

Code

#include "Graph.hpp"
#include "GraphMisc.hpp"

template<typename WeightType>
class BellmanFord{
    public:
    BellmanFord(Graph<WeightType> &graph, Vertex s = -1) :
        G(graph), V(graph.VertexSize()), dist_(V){
        if(s != -1) Solve(s);
    }

    inline bool Reachable(const Vertex &t) const {
        return dist_[t] != inf;
    }

    inline WeightType Distance(const Vertex &t) const {
        return dist_[t];
    }

    inline bool NegativeCycle() const {
        return negative_cycle_;
    }

    void Solve(Vertex s){
        fill(dist_.begin(), dist_.end(), inf);
        dist_[s] = WeightType(0);
        negative_cycle_ = false;
        int update_count = 0;
        auto E = ConvertEdgeSet(G);
        while(1){
            if(update_count == V){
                negative_cycle_ = true;
                break;
            }
            bool update_flag = false;
            for(const Edge<WeightType> &e : E){
                if(dist_[e.from] == inf) continue;
                if(dist_[e.to] > dist_[e.from] + e.cost){
                    dist_[e.to] = dist_[e.from] + e.cost;
                    update_flag = true;
                }
            }
            if(!update_flag) break;
            ++update_count;
        }
    }

    inline WeightType operator[](const Vertex &t){
        return dist_[t];
    }

    inline const WeightType operator[](const Vertex &t) const {
        return dist_[t];
    }

    private:
    Graph<WeightType> &G;
    int V;
    WeightType inf{WeightType(INF)};
    bool negative_cycle_;
    vector<WeightType> dist_;
};

#line 2 "Library/Graph/Graph.hpp"

#line 2 "Library/Common.hpp"

/**
 * @file Common.hpp
 */

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cstdint>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

using ll = int64_t;
using ull = uint64_t;

constexpr const ll INF = (1LL << 62) - (3LL << 30) - 1;
#line 4 "Library/Graph/Graph.hpp"

using Vertex = int;

template<typename WeightType = int32_t>
struct Edge{
    public:
    Edge() = default;

    Edge(Vertex from_, Vertex to_, WeightType weight_ = 1, int idx_ = -1) :
        from(from_), to(to_), cost(weight_), idx(idx_){}
    
    bool operator<(const Edge<WeightType> &e) const {return cost < e.cost;}

    operator int() const {return to;}

    Vertex from, to;
    WeightType cost;
    int idx;
};

template<typename WeightType = int32_t>
class Graph{
    public:
    Graph() = default;

    Graph(int V) : edge_size_(0), adjacent_list_(V){}
    
    inline void AddUndirectedEdge(Vertex u, Vertex v, WeightType w = 1){
        int idx = edge_size_++;
        adjacent_list_[u].push_back(Edge<WeightType>(u, v, w, idx));
        adjacent_list_[v].push_back(Edge<WeightType>(v, u, w, idx));
    }
    
    inline void AddDirectedEdge(Vertex u, Vertex v, WeightType w = 1){
        int idx = edge_size_++;
        adjacent_list_[u].push_back(Edge<WeightType>(u, v, w, idx));
    }

    inline size_t VertexSize() const {
        return adjacent_list_.size();
    }

    inline size_t EdgeSize() const {
        return edge_size_;
    }

    inline vector<Edge<WeightType>> &operator[](const Vertex v){
        return adjacent_list_[v];
    }

    inline const vector<Edge<WeightType>> &operator[](const Vertex v) const {
        return adjacent_list_[v];
    }
    
    private:
    size_t edge_size_;
    vector<vector<Edge<WeightType>>> adjacent_list_;
};

template<typename WeightType = int32_t>
Graph<WeightType> InputGraph(int N, int M, int padding = -1, bool weighted = false, bool directed = false){
    Graph<WeightType> G(N);
    for(int i = 0; i < M; ++i){
        Vertex u, v; WeightType w = 1;
        cin >> u >> v, u += padding, v += padding;
        if(weighted) cin >> w;
        if(directed) G.AddDirectedEdge(u, v, w);
        else G.AddUndirectedEdge(u, v, w);
    }
    return G;
}
#line 2 "Library/Graph/GraphMisc.hpp"

#line 4 "Library/Graph/GraphMisc.hpp"

template<typename WeightType>
vector<Edge<WeightType>> ConvertEdgeSet(const Graph<WeightType> &G){
    vector<Edge<WeightType>> ret;
    vector<bool> check(G.EdgeSize(), false);
    int n = G.VertexSize();
    for(int u = 0; u < n; ++u){
        for(const Edge<WeightType> &e : G[u]){
            if(check[e.idx]) continue;
            check[e.idx] = true;
            ret.push_back(e);
        }
    }
    return ret;
}

template<typename WeightType>
vector<vector<WeightType>> ConvertDistanceMatrix(const Graph<WeightType> &G){
    int n = G.VertexSize();
    vector<vector<WeightType>> ret(n, vector<WeightType>(n, WeightType(INF)));
    for(int u = 0; u < n; ++u){
        ret[u][u] = WeightType(0);
        for(const Edge<WeightType> &e : G[u]){
            ret[u][e.to] = e.cost;
        }
    }
    return ret;
}

template<typename WeightType>
Graph<WeightType> ReverseGraph(const Graph<WeightType> &G){
    int n = G.VertexSize();
    Graph<WeightType> ret(n);
    for(int u = 0; u < n; ++u){
        for(const Edge<WeightType> &e : G[u]){
            ret.AddDirectedEdge(e.to, e.from, e.cost);
        }
    }
    return ret;
}
#line 3 "Library/Graph/BellmanFord.hpp"

template<typename WeightType>
class BellmanFord{
    public:
    BellmanFord(Graph<WeightType> &graph, Vertex s = -1) :
        G(graph), V(graph.VertexSize()), dist_(V){
        if(s != -1) Solve(s);
    }

    inline bool Reachable(const Vertex &t) const {
        return dist_[t] != inf;
    }

    inline WeightType Distance(const Vertex &t) const {
        return dist_[t];
    }

    inline bool NegativeCycle() const {
        return negative_cycle_;
    }

    void Solve(Vertex s){
        fill(dist_.begin(), dist_.end(), inf);
        dist_[s] = WeightType(0);
        negative_cycle_ = false;
        int update_count = 0;
        auto E = ConvertEdgeSet(G);
        while(1){
            if(update_count == V){
                negative_cycle_ = true;
                break;
            }
            bool update_flag = false;
            for(const Edge<WeightType> &e : E){
                if(dist_[e.from] == inf) continue;
                if(dist_[e.to] > dist_[e.from] + e.cost){
                    dist_[e.to] = dist_[e.from] + e.cost;
                    update_flag = true;
                }
            }
            if(!update_flag) break;
            ++update_count;
        }
    }

    inline WeightType operator[](const Vertex &t){
        return dist_[t];
    }

    inline const WeightType operator[](const Vertex &t) const {
        return dist_[t];
    }

    private:
    Graph<WeightType> &G;
    int V;
    WeightType inf{WeightType(INF)};
    bool negative_cycle_;
    vector<WeightType> dist_;
};

Bellman Ford - ベルマンフォード法 (Library/Graph/BellmanFord.hpp)

Bellman Ford - ベルマンフォード法

Function

Constructor

Reachable

Distance

NegativeCycle

Solve

operator[]

Depends on

Verified with

Code

Bellman Ford - ベルマンフォード法
(Library/Graph/BellmanFord.hpp)